# Problem of the Week Problem B and Solution 'Temp'ting Crickets

## Problem

Crickets can help determine the temperature, in degrees Celsius. One possible way to make this calculation is to follow the steps below.

• Step 1: Count the number of chirps in $$25$$ seconds.

• Step 2: Divide the number from Step 1 by $$3$$.

• Step 3: Add $$4$$ to the number from Step 2.

1. By filling in each $$\underline{\ \ \ \ \ }$$ in the following equation with either a variable or a number, write an equation to show how to get the temperature, $$t$$, based on a certain number of chirps, $$c$$, in $$25$$ seconds. $t = \underline{\ \ \ \ \ }\div \underline{\ \ \ \ \ }+\underline{\ \ \ \ \ }$

2. Fill in the second column of the following table.

Chirps ($$c$$) in $$25$$ seconds Temperature ($$t$$) in degrees Celsius
$$60$$
$$54$$
$$66$$
3. Fill in the first column of the following table.

Chirps ($$c$$) in $$25$$ seconds Temperature ($$t$$) in degrees Celsius
$$18$$
$$20$$
$$16$$

## Solution

1. To determine the temperature, $$t$$, we take the number of chirps in $$25$$ seconds, $$c$$, divide by $$3$$, then add $$4$$. That is, $$t = \underline{\,c\,}\div\underline{\,3\,}+\underline{\,4\,}$$.

2. You may use the given steps or the equation from part (a) to fill in the table.

For example when there are $$60$$ chirps, we divide by $$3$$ to get $$20$$, and then add $$4$$ to get $$24$$ degrees Celsius.

Or we may use the equation $$t = 60 \div 3 + 4 = 20 + 4 = 24$$.

Chirps ($$c$$) in $$25$$ seconds Temperature ($$t$$) in degrees Celsius
$$60$$ $$24$$
$$54$$ $$22$$
$$66$$ $$26$$
3. To find the number of chirps for a given temperature, we work backwards, reversing the steps as we go. That is, we subtract $$4$$ from the given temperature, and then multiply by $$3$$.

For example when the temperature is $$18$$ degrees Celsius, we subtract $$4$$ to get $$14$$, and then multiply $$14$$ by $$3$$ to get $$42$$ chirps.

The equation to calculate chirps, $$c$$, given temperature, $$t$$, is $$c=(t-4)\times 3$$.

Chirps ($$c$$) in $$25$$ seconds Temperature ($$t$$) in degrees Celsius
$$42$$ $$18$$
$$48$$ $$20$$
$$36$$ $$16$$